\[ \boxed { {\frac {\rm d}{{\rm d}x}}y \left ( x \right ) ={\frac { \left ( -108\,{x}^{3/2}y \left ( x \right ) +18\,{x}^{9/2}-108\,{x}^{3/2}-216\, \left ( y \left ( x \right ) \right ) ^{3}+108\,{x}^{3} \left ( y \left ( x \right ) \right ) ^{2}-18\,y \left ( x \right ) {x}^{6}+{x}^{9} \right ) \sqrt {x}}{-216\,y \left ( x \right ) +36\,{x}^{3}-216}}=0} \]
Mathematica: cpu = 0.027003 (sec), leaf count = 79 \[ \left \{\left \{y(x)\to \frac {1}{6} \left (x^3-6\right )-\frac {1}{216 \left (-\frac {1}{\sqrt {c_1-62208 x^{3/2}}}-\frac {1}{216}\right )}\right \},\left \{y(x)\to \frac {1}{6} \left (x^3-6\right )-\frac {1}{216 \left (\frac {1}{\sqrt {c_1-62208 x^{3/2}}}-\frac {1}{216}\right )}\right \}\right \} \]
Maple: cpu = 0.062 (sec), leaf count = 85 \[ \left \{ y \left ( x \right ) ={\frac {1}{6} \left ( \sqrt {9\,{\it \_C1} -12\,{x}^{3/2}}{x}^{3}-3\,{x}^{3}+18 \right ) \left ( -3+\sqrt {9\,{ \it \_C1}-12\,{x}^{3/2}} \right ) ^{-1}},y \left ( x \right ) ={\frac {1 }{6} \left ( \sqrt {9\,{\it \_C1}-12\,{x}^{3/2}}{x}^{3}+3\,{x}^{3}-18 \right ) \left ( 3+\sqrt {9\,{\it \_C1}-12\,{x}^{3/2}} \right ) ^{-1}} \right \} \]